Answer:
x = sqrt(89)/10 - 3/10 or x = -3/10 - sqrt(89)/10
Explanation:
Solve for x over the real numbers:
5 x^2 + 3 x - 4 = 0
Divide both sides by 5:
x^2 + (3 x)/5 - 4/5 = 0
Add 4/5 to both sides:
x^2 + (3 x)/5 = 4/5
Add 9/100 to both sides:
x^2 + (3 x)/5 + 9/100 = 89/100
Write the left hand side as a square:
(x + 3/10)^2 = 89/100
Take the square root of both sides:
x + 3/10 = sqrt(89)/10 or x + 3/10 = -sqrt(89)/10
Subtract 3/10 from both sides:
x = sqrt(89)/10 - 3/10 or x + 3/10 = -sqrt(89)/10
Subtract 3/10 from both sides:
Answer: x = sqrt(89)/10 - 3/10 or x = -3/10 - sqrt(89)/10